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    Coursera
    1. Calculus and Optimization for Machine Learning
    2. Week 5
    3. Fifth Week Final Test
    PreviousNext
      • Completed
        Video: LectureIntroduction to the Week
        . Duration: 5 minutes5 min
      • Completed
        Video: LectureAntiderivative: Definition
        . Duration: 5 minutes5 min
      • Completed
        Video: LectureAntiderivative: Table of Integrals
        . Duration: 6 minutes6 min
      • Completed
        Video: LectureChange of Variable and Integration by Parts
        . Duration: 14 minutes14 min
      • Completed
        Video: LectureAntiderivative: Examples
        . Duration: 10 minutes10 min
      • Completed
        Interactive Plot: Piecewise Integration
        . Duration: 15 minutes15 min
      • Completed
        Video: LectureIntegrability in Elementary Functions
        . Duration: 13 minutes13 min
      • Completed
        Practice Quiz: Practice Quiz #1
        4 questions
      • Completed
        Video: LectureDefinite Integral
        . Duration: 9 minutes9 min
      • Completed
        Video: LectureDefinite Integral: Existence
        . Duration: 6 minutes6 min
      • Completed
        Video: LectureDefinite Integral: Sufficient Conditions
        . Duration: 7 minutes7 min
      • Completed
        Video: LectureFundamental Theorem of Calculus
        . Duration: 8 minutes8 min
      • Completed
        Interactive Plot: Fundamental Theorem of Calculus
        . Duration: 15 minutes15 min
      • Completed
        Video: LectureImproper Integrals
        . Duration: 9 minutes9 min
      • Completed
        Video: LectureImproper Integrals: Examples and Comparison Rule
        . Duration: 14 minutes14 min
      • Completed
        Video: LectureNumerical Methods of Integration
        . Duration: 8 minutes8 min
      • Completed
        Interactive Plot: Numerical Integration
        . Duration: 15 minutes15 min
      • Completed
        Practice Quiz: Practice Quiz #2
        4 questions
      • Completed
        Quiz: Fifth Week Final Test
        7 questions
    QuizQuiz • 1h1 hour

    Fifth Week Final Test

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    Fifth Week Final Test
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    1.
    Question 1

    For any given function f(x)f(x)f(x) and its antiderivative F(x)F(x)F(x) it is true that:

    1 / 1 point
    Check
    Correct

    Correct!

    Check
    Correct

    Correct!

    2.
    Question 2

    Compute an antiderivative F(x)F(x)F(x) of f(x)=(x−1)/xf(x)=(x-1)/\sqrt{x}f(x)=(x−1)/x​ such as F(0)=0F(0)=0F(0)=0. Write F(1)F(1)F(1).

    1 / 1 point
    −43- \frac{4}{3}−34​
    -4/3
    Check
    Correct

    The indefinite integral is F(x)=23(x−3)x+CF(x)=\frac{2}{3}(x-3)\sqrt{x}+CF(x)=32​(x−3)x​+C.

    3.
    Question 3

    Compute an antiderivative F(x)F(x)F(x) of

    f(x)={−sinx,if x≥01−x2,if x<0

    such as F(0)=1F(0)=1F(0)=1 and F(π/2)=0F(\pi /2)=0F(π/2)=0. Write F(π)+F(−1)F(\pi)+F(-1)F(π)+F(−1).

    1 / 1 point
    −23- \frac{2}{3}−32​
    -2/3
    Check
    Correct
    4.
    Question 4

    Compute I=∫01arcsin⁡xI=\int_{0}^{1}\arcsin xI=∫01​arcsinx. Write (I+1)/π(I+1)/\pi(I+1)/π, round up by 2 digits.

    1 / 1 point
    0.50.50.5
    .5
    Check
    Correct
    5.
    Question 5

    Compute I=∫ee2dx/(x⋅ln⁡x)I=\int_e^{e^2} dx/(x\cdot \ln x)I=∫ee2​dx/(x⋅lnx). Write eIe^IeI.

    1 / 1 point
    222
    2
    Check
    Correct
    6.
    Question 6

    Choose correct statements about improper integrals:

    1 / 1 point
    Check
    Correct
    7.
    Question 7

    Find improper integral: ∫0+∞x⋅e−xdx\int_0^{+\infty} x \cdot e^{-x} dx∫0+∞​x⋅e−xdx.

    1 / 1 point
    111
    1
    Check
    Correct